public class Partitioning extends Object
The algorithms partition arrays into two or more intervals. They distinguish between synchronously partitioning either one, two or three arrays. They further come in templated versions, either partitioning int[] arrays or double[] arrays.
You may want to start out reading about the simplest case: Partitioning one int[] array into two intervals.
To do so, read partition(int[],int,int,int)
.
Next, building upon that foundation comes a method partitioning int[] arrays into multiple intervals.
See partition(int[],int,int,int[],int,int,int[])
for related documentation.
All other methods are no different than the one's you now already understand, except that they operate on slightly different data types.
Performance
Partitioning into two intervals is O( N ). Partitioning into k intervals is O( N * log(k)). Constants factors are minimized. No temporary memory is allocated; Partitioning is inplace.
Partitioning
Modifier and Type  Field and Description 

protected static int 
steps 
static int 
swappedElements 
Modifier  Constructor and Description 

protected 
Partitioning()
Makes this class non instantiable, but still let's others inherit from it.

Modifier and Type  Method and Description 

static int 
dualPartition(double[] list,
double[] secondary,
int from,
int to,
double splitter)
Same as
dualPartition(int[],int[],int,int,int)
except that it synchronously partitions double[] rather than int[] arrays. 
static void 
dualPartition(double[] list,
double[] secondary,
int from,
int to,
double[] splitters,
int splitFrom,
int splitTo,
int[] splitIndexes)
Same as
dualPartition(int[],int[],int,int,int[],int,int,int[])
except that it synchronously partitions double[] rather than int[] arrays. 
static int 
dualPartition(int[] list,
int[] secondary,
int from,
int to,
int splitter)
Same as
partition(int[],int,int,int) except that this method synchronously partitions two arrays at the same time;
both arrays are partially sorted according to the elements of the primary array. 
static void 
dualPartition(int[] list,
int[] secondary,
int from,
int to,
int[] splitters,
int splitFrom,
int splitTo,
int[] splitIndexes)
Same as
partition(int[],int,int,int[],int,int,int[]) except that this method synchronously partitions two arrays at the same time;
both arrays are partially sorted according to the elements of the primary array. 
static void 
genericPartition(int from,
int to,
int splitFrom,
int splitTo,
int[] splitIndexes,
IntComparator comp,
IntComparator comp2,
IntComparator comp3,
Swapper swapper)
Same as
partition(int[],int,int,int[],int,int,int[])
except that it generically partitions arbitrary shaped data (for example matrices or multiple arrays) rather than int[] arrays. 
static int 
partition(double[] list,
int from,
int to,
double splitter)
Same as
partition(int[],int,int,int)
except that it partitions double[] rather than int[] arrays. 
static void 
partition(double[] list,
int from,
int to,
double[] splitters,
int splitFrom,
int splitTo,
int[] splitIndexes)
Same as
partition(int[],int,int,int[],int,int,int[])
except that it partitions double[] rather than int[] arrays. 
static void 
partition(DoubleArrayList list,
int from,
int to,
DoubleArrayList splitters,
IntArrayList splitIndexes)
Equivalent to partition(list.elements(), from, to, splitters.elements(), 0, splitters.size()1, splitIndexes.elements()).

static int 
partition(int[] list,
int from,
int to,
int splitter)
Partitions (partially sorts) the given list such that all elements falling into the given interval are placed next to each other.

static void 
partition(int[] list,
int from,
int to,
int[] splitters,
int splitFrom,
int splitTo,
int[] splitIndexes)
Partitions (partially sorts) the given list such that all elements falling into some intervals are placed next to each other.

static void 
partition(IntArrayList list,
int from,
int to,
IntArrayList splitters,
IntArrayList splitIndexes)
Equivalent to partition(list.elements(), from, to, splitters.elements(), 0, splitters.size()1, splitIndexes.elements()).

static void 
partition(Object[] list,
int from,
int to,
Object[] splitters,
int splitFrom,
int splitTo,
int[] splitIndexes,
Comparator comp)
Same as
partition(int[],int,int,int[],int,int,int[])
except that it partitions Object[] rather than int[] arrays. 
static int 
partition(Object[] list,
int from,
int to,
Object splitter,
Comparator comp)
Same as
partition(int[],int,int,int)
except that it synchronously partitions the objects of the given list by the order of the given comparator. 
static int 
triplePartition(double[] list,
double[] secondary,
double[] tertiary,
int from,
int to,
double splitter)
Same as
triplePartition(int[],int[],int[],int,int,int)
except that it synchronously partitions double[] rather than int[] arrays. 
static void 
triplePartition(double[] list,
double[] secondary,
double[] tertiary,
int from,
int to,
double[] splitters,
int splitFrom,
int splitTo,
int[] splitIndexes)
Same as
triplePartition(int[],int[],int[],int,int,int[],int,int,int[])
except that it synchronously partitions double[] rather than int[] arrays. 
static int 
triplePartition(int[] list,
int[] secondary,
int[] tertiary,
int from,
int to,
int splitter)
Same as
partition(int[],int,int,int) except that this method synchronously partitions three arrays at the same time;
all three arrays are partially sorted according to the elements of the primary array. 
static void 
triplePartition(int[] list,
int[] secondary,
int[] tertiary,
int from,
int to,
int[] splitters,
int splitFrom,
int splitTo,
int[] splitIndexes)
Same as
partition(int[],int,int,int[],int,int,int[]) except that this method synchronously partitions three arrays at the same time;
all three arrays are partially sorted according to the elements of the primary array. 
protected Partitioning()
public static void dualPartition(double[] list, double[] secondary, int from, int to, double[] splitters, int splitFrom, int splitTo, int[] splitIndexes)
dualPartition(int[],int[],int,int,int[],int,int,int[])
except that it synchronously partitions double[] rather than int[] arrays.public static int dualPartition(double[] list, double[] secondary, int from, int to, double splitter)
dualPartition(int[],int[],int,int,int)
except that it synchronously partitions double[] rather than int[] arrays.public static void dualPartition(int[] list, int[] secondary, int from, int to, int[] splitters, int splitFrom, int splitTo, int[] splitIndexes)
partition(int[],int,int,int[],int,int,int[])
except that this method synchronously partitions two arrays at the same time;
both arrays are partially sorted according to the elements of the primary array.
In other words, each time an element in the primary array is moved from index A to B, the correspoding element within the secondary array is also moved from index A to B.
Use cases:
Image having a large list of 2dimensional points. If memory consumption and performance matter, it is a good idea to physically lay them out as two 1dimensional arrays (using something like Point2D objects would be prohibitively expensive, both in terms of time and space). Now imagine wanting to histogram the points. We may want to partially sort the points by xcoordinate into intervals. This method efficiently does the job.
Performance:
Same as for singlepartition methods.
public static int dualPartition(int[] list, int[] secondary, int from, int to, int splitter)
partition(int[],int,int,int)
except that this method synchronously partitions two arrays at the same time;
both arrays are partially sorted according to the elements of the primary array.
In other words, each time an element in the primary array is moved from index A to B, the correspoding element within the secondary array is also moved from index A to B.
Performance:
Same as for singlepartition methods.
public static void genericPartition(int from, int to, int splitFrom, int splitTo, int[] splitIndexes, IntComparator comp, IntComparator comp2, IntComparator comp3, Swapper swapper)
partition(int[],int,int,int[],int,int,int[])
except that it generically partitions arbitrary shaped data (for example matrices or multiple arrays) rather than int[] arrays.
This method operates on arbitrary shaped data and arbitrary shaped splitters. In fact, it has no idea what kind of data by what kind of splitters it is partitioning. Comparisons and swapping are delegated to user provided objects which know their data and can do the job.
Lets call the generic data g (it may be a matrix, one array, three linked lists
or whatever). Lets call the generic splitters s.
This class takes a user comparison function operating on two indexes
(a,b), namely an IntComparator
.
The comparison function determines whether s[a] is equal, less or greater than g[b].
This method can then decide to swap the data g[b]
with the data g[c] (yes, c, not a).
It calls a user provided Swapper
object that knows how to swap the data of these two indexes.
Again, note the details: Comparisons compare s[a] with g[b]. Swaps swap g[b] with g[c]. Prior to calling this method, the generic splitters s must be sorted ascending and must not contain multiple equal values. These preconditions are not checked; be sure that they are met.
from
 the index of the first element within g to be considered.to
 the index of the last element within g to be considered.
The method considers the elements g[from] .. g[to].splitFrom
 the index of the first splitter element to be considered.splitTo
 the index of the last splitter element to be considered.
The method considers the splitter elements s[splitFrom] .. s[splitTo].splitIndexes
 a list into which this method fills the indexes of elements delimiting intervals.
Upon return splitIndexes[splitFrom..splitTo] will be set accordingly.
Therefore, must satisfy splitIndexes.length > splitTo.comp
 the comparator comparing a splitter with an element of the generic data.
Takes as first argument the index a within the generic splitters s.
Takes as second argument the index b within the generic data g.comp2
 the comparator to determine the order of the generic data.
Takes as first argument the index a within the generic data g.
Takes as second argument the index b within the generic data g.comp3
 the comparator comparing a splitter with another splitter.
Takes as first argument the index a within the generic splitters s.
Takes as second argument the index b within the generic splitters g.swapper
 an object that knows how to swap the elements at any two indexes (a,b).
Takes as first argument the index b within the generic data g.
Takes as second argument the index c within the generic data g.
Tip: Normally you will have splitIndexes.length == s.length as well as from==0, to==g.length1 and splitFrom==0, splitTo==s.length1.
Sort
,
Sort#sort(int,int,IntComparator,Swapper)
,
Sorting.binarySearchFromTo(int,int,IntComparator)
public static void partition(double[] list, int from, int to, double[] splitters, int splitFrom, int splitTo, int[] splitIndexes)
partition(int[],int,int,int[],int,int,int[])
except that it partitions double[] rather than int[] arrays.public static int partition(double[] list, int from, int to, double splitter)
partition(int[],int,int,int)
except that it partitions double[] rather than int[] arrays.public static void partition(int[] list, int from, int to, int[] splitters, int splitFrom, int splitTo, int[] splitIndexes)
Example:
list = (7, 4, 5, 50, 6, 4, 3, 6), splitters = (5, 10, 30) defines the three intervals [infinity,5), [5,10), [10,30). Lets define to sort the entire list (from=0, to=7) using all splitters (splitFrom==0, splitTo=2).
The method modifies the list to be list = (4, 4, 3, 6, 7, 5, 6, 50) and returns the splitIndexes = (2, 6, 6). In other words,
More formally, this method guarantees that upon return for all j = splitFrom .. splitTo there holds:
for all i = splitIndexes[j1]+1 .. splitIndexes[j]: splitters[j1] <= list[i] < splitters[j].
Performance:
Let N=tofrom+1 be the number of elements to be partitioned. Let k=splitTosplitFrom+1 be the number of splitter elements. Then we have the following time complexities
Implementation:
The algorithm can be seen as a Bentley/McIlroy quicksort where swapping and insertion sort are omitted. It is designed to detect and take advantage of skew while maintaining good performance in the uniform case.
list
 the list to be partially sorted.from
 the index of the first element within list to be considered.to
 the index of the last element within list to be considered.
The method considers the elements list[from] .. list[to].splitters
 the values at which the list shall be split into intervals.
Must be sorted ascending and must not contain multiple identical values.
These preconditions are not checked; be sure that they are met.splitFrom
 the index of the first splitter element to be considered.splitTo
 the index of the last splitter element to be considered.
The method considers the splitter elements splitters[splitFrom] .. splitters[splitTo].splitIndexes
 a list into which this method fills the indexes of elements delimiting intervals.
Upon return splitIndexes[splitFrom..splitTo] will be set accordingly.
Therefore, must satisfy splitIndexes.length > splitTo.
Tip: Normally you will have splitIndexes.length == splitters.length as well as from==0, to==list.length1 and splitFrom==0, splitTo==splitters.length1.
Arrays
,
GenericSorting
,
Arrays
public static int partition(int[] list, int from, int to, int splitter)
Example:
list = (7, 4, 5, 50, 6, 4, 3, 6), splitter = 5 defines the two intervals [infinity,5), [5,+infinity].
The method modifies the list to be list = (4, 4, 3, 50, 6, 7, 5, 6) and returns the split index 2. In other words,
More formally, this method guarantees that upon return there holds:
Performance:
Let N=tofrom+1 be the number of elements to be partially sorted. Then the time complexity is O( N ). No temporary memory is allocated; the sort is inplace.
list
 the list to be partially sorted.from
 the index of the first element within list to be considered.to
 the index of the last element within list to be considered.
The method considers the elements list[from] .. list[to].splitter
 the value at which the list shall be split.public static void partition(Object[] list, int from, int to, Object[] splitters, int splitFrom, int splitTo, int[] splitIndexes, Comparator comp)
partition(int[],int,int,int[],int,int,int[])
except that it partitions Object[] rather than int[] arrays.public static int partition(Object[] list, int from, int to, Object splitter, Comparator comp)
partition(int[],int,int,int)
except that it synchronously partitions the objects of the given list by the order of the given comparator.public static void partition(DoubleArrayList list, int from, int to, DoubleArrayList splitters, IntArrayList splitIndexes)
public static void partition(IntArrayList list, int from, int to, IntArrayList splitters, IntArrayList splitIndexes)
public static void triplePartition(double[] list, double[] secondary, double[] tertiary, int from, int to, double[] splitters, int splitFrom, int splitTo, int[] splitIndexes)
triplePartition(int[],int[],int[],int,int,int[],int,int,int[])
except that it synchronously partitions double[] rather than int[] arrays.public static int triplePartition(double[] list, double[] secondary, double[] tertiary, int from, int to, double splitter)
triplePartition(int[],int[],int[],int,int,int)
except that it synchronously partitions double[] rather than int[] arrays.public static void triplePartition(int[] list, int[] secondary, int[] tertiary, int from, int to, int[] splitters, int splitFrom, int splitTo, int[] splitIndexes)
partition(int[],int,int,int[],int,int,int[])
except that this method synchronously partitions three arrays at the same time;
all three arrays are partially sorted according to the elements of the primary array.
In other words, each time an element in the primary array is moved from index A to B, the correspoding element within the secondary array as well as the corresponding element within the tertiary array are also moved from index A to B.
Use cases:
Image having a large list of 3dimensional points. If memory consumption and performance matter, it is a good idea to physically lay them out as three 1dimensional arrays (using something like Point3D objects would be prohibitively expensive, both in terms of time and space). Now imagine wanting to histogram the points. We may want to partially sort the points by xcoordinate into intervals. This method efficiently does the job.
Performance:
Same as for singlepartition methods.
public static int triplePartition(int[] list, int[] secondary, int[] tertiary, int from, int to, int splitter)
partition(int[],int,int,int)
except that this method synchronously partitions three arrays at the same time;
all three arrays are partially sorted according to the elements of the primary array.
In other words, each time an element in the primary array is moved from index A to B, the correspoding element within the secondary array as well as the corresponding element within the tertiary array are also moved from index A to B.
Performance:
Same as for singlepartition methods.
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